For "Airborne" sound, and, to some extent "Impact" sound, you need to add density to your existing wall(s).
Building a concrete block wall up against the existing one would be wonderful ............. but highly impracticable.
So, bare minimum would be adding two layers of 12.5mm plasterboard.
Much better, one or two layers of 12.5mm "Soundcheck" board...
https://www.diy.com/departments/gyproc-soundbloc-tapered-edge-plasterboard-l-2-4m-w-1-2m-t-12-5mm/35771_BQ.prd?ds_rl=1272379&ds_rl=1272409&ds_rl=1272379&gclid=Cj0KCQiAtf_tBRDtARIsAIbAKe16ik5TC4q-T8VitoO_Cl5y7Ib6k6aDxh1QaQPoMKzf0HEW5YryQygaAoW2EALw_wcB&gclsrc=aw.ds
Even better... build a timber stud wall up against the existing (100x50 mm studs)
Fill between the studs with "Rockwool" insulation.
Then board with Soundcheck, and finish it with a "Dry lining plastering system". It's very easy. a wide spreader is used to apply a jointing compound to the joints only. Then paper tape and a sponge to finish. (See Youtube.)
The big faff is dealing with sockets and skirting boards. All pretty straightforward though.